Performability analysis of parallel and distributed algorithms

A generalized stochastic Petri net (GSPN) performability model of a parallel and distributed computation is developed. The performance-related activities such as computations and communications are orders of magnitude faster than the component failure and repair activities. Based on the notion of time-scale decomposition, a hierarchy of two levels is defined. At the lower level the performance submodel describes the activities in the application program, while at the higher level the component failure and repair submodel for the underlying architecture defines the current configuration of processors and communication links available for the computation. These two submodels define the reward model needed for performability analysis. Two parallel FFT (fast Fourier transform) algorithms on a hypercube architecture are presented to illustrate the above modeling technique. A general and extended reliability model of the hypercube is also developed. Various performability measures are presented to demonstrate the importance of performability evaluation for mission-critical parallel applications.<>